BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 3.3, Problem 10E
To determine

Find the differentiate form of the given equation.

Expert Solution

Answer to Problem 10E

The differentiate form of the given equationis dydx=xcosx(x+cosx)2 .

Explanation of Solution

Given:

The given equationis y=1+sinxx+cosx .

Calculation:

  (fg)'=gf'fg'g2

  y=1+sinxx+cosxdydx=(x+cosx)ddx(1+sinx)(1+sinx)ddx(x+cosx)(x+cosx)2

Use the rule ddx(x)=1 , ddx(cosx)=sinx and ddx(sinx)=cosx

  dydx=(x+cosx)ddx(1+sinx)(1+sinx)ddx(x+cosx)(x+cosx)2dydx=(x+cosx)(0+cosx)(1+sinx)(1sinx)(x+cosx)2dydx=xcosx+cos2x(1sin2x)(x+cosx)2dydx=xcosx+cos2x1+sin2x(x+cosx)2dydx=xcosx+(cos2x+sin2x)1(x+cosx)2dydx=xcosx+11(x+cosx)2dydx=xcosx(x+cosx)2

Hence the differentiate form of the given equationis dydx=xcosx(x+cosx)2 .

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